A371363
Expansion of (1/x) * Series_Reversion( x * (1-3*x)^3 / (1-2*x) ).
Original entry on oeis.org
1, 7, 85, 1261, 20788, 365845, 6731758, 127938625, 2491921516, 49480794460, 997897366717, 20384025765619, 420869454302620, 8769197604091246, 184151509243984300, 3893585866824069577, 82817275938125471548, 1770880435886367151060
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^3/(1-2*x))/x)
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a(n) = sum(k=0, n, 2^(n-k)*binomial(3*n+k+2, k)*binomial(3*n+1, n-k))/(n+1);
A371365
Expansion of (1/x) * Series_Reversion( x * (1-4*x)^3 / (1-3*x) ).
Original entry on oeis.org
1, 9, 141, 2701, 57513, 1307553, 31083925, 763267077, 19208408721, 492817411705, 12842067417309, 338956669920189, 9042967461581753, 243464712274093713, 6606427290991922277, 180492205687604057013, 4960765361688213527073
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^3/(1-3*x))/x)
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a(n) = sum(k=0, n, 3^(n-k)*binomial(3*n+k+2, k)*binomial(3*n+1, n-k))/(n+1);
A369024
Expansion of (1/x) * Series_Reversion( x * (1-2*x)^4 / (1-x) ).
Original entry on oeis.org
1, 7, 81, 1135, 17617, 291479, 5038177, 89901023, 1643514849, 30623478951, 579444828465, 11103818394447, 215053322179121, 4202849976054583, 82778942956393409, 1641477474636943295, 32743892109730116801, 656612555241354578759, 13228883898856161274129
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^4/(1-x))/x)
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a(n, s=1, t=4, u=-1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Showing 1-3 of 3 results.